Re: Godel's Theorem under Fuzzy Logic?

Stephen Paul King (
Tue, 28 Apr 1998 18:12:32 +0200 (MET DST)

Dear Prof.

Is there a preprint available in postscript of this paper?


Stephen Paul King

On 20 Apr 1998 12:43:34 GMT, you wrote:

>In some paper we define and study the notion of recursive enumerability for
>fuzzy subsets and the one of productive or creative fuzzy subset.
>Also, we prove that if a fuzzy logic is "universal" (i.e. able to represent
>any recursive enumerable fuzzy set) then in such a logic Goedel limitative
>theorems holds. Nevertheless we was not able to give a good example of
>"universal fuzzy logic". In any case I suggest to read
**>L. Biacino and G. Gerla, Decidability, recursive enumerability and
>Hierarchy for L-subsets, Z. Math. Logik Grund. Math. 35 1989.
>where some limitative theorem is given.
>See also
**>L. Biacino and G. Gerla, Fuzzy sets: a constructive approach. Fuzzy
Sets and
>Systems 45 (1992).
>At 04.02 06/04/98 +0200, you wrote:
>>Christian Borgelt <> writes:
>> >Completeness means that starting from the axioms and applying only
>> >the allowed inference rules you can, in principle, prove any true
>> >formula of the formal system.
>> No it doesn't. Completeness is a syntactic concept: for every A,
>>A or the negation of A is provable in T.
>> >Another difficulty, which is not limited to fuzzy logic, is whether
>> >G"odel's proof is actually a proof. To prove incompleteness, we have
>> >to interpret the formula and have to understand that what it says is
>> >true. That is, the result is not achieved by formal reasoning, but
>> >by some meta-reasoning done from outside the system.
>> This is a misunderstanding. Godel's theorem for a theory T is
>>an ordinary mathematical theorem, provable (for standard theories
>>T) in T itself.